reserve A for preIfWhileAlgebra,
  C,I,J for Element of A;
reserve S for non empty set,
  T for Subset of S,
  s for Element of S;

theorem Th54:
  len ECIW-signature = 4 & dom ECIW-signature = Seg 4 &
  ECIW-signature.1 = 0 & ECIW-signature.2 = 2 &
  ECIW-signature.3 = 3 & ECIW-signature.4 = 2
proof
A1: len <*0,2*> = 2 by FINSEQ_1:44;
A2: len <*3,2*> = 2 by FINSEQ_1:44;
A3: dom <*0,2*> = Seg 2 by A1,FINSEQ_1:def 3;
A4: dom <*3,2*> = Seg 2 by A2,FINSEQ_1:def 3;
  then
A5: 1 in dom <*3,2*>;
A6: <*3,2*>.1 = 3;
A7: 2 in dom <*3,2*> by A4;
A8: <*3,2*>.2 = 2;
A9: 2+1 = 3;
A10: 1 in dom <*0,2*> by A3;
A11: <*0,2*>.1 = 0;
A12: 2 in dom <*0,2*> by A3;
  <*0,2*>.2 = 2;
  hence thesis by A1,A2,A5,A6,A7,A8,A9,A10,A11,A12,FINSEQ_1:22,def 7;
end;
